Laptop for pharmacy school; long battery life; small screen

I am looking for a laptop for pharmacy school. Everything regarding notes, tests, etc are all online. What I am looking for specifically will have a long battery life, hopefully over 5 hours, my current is an hour tops, and a small screen, roughly 13 inches, current is 17. It will be mainly used for school with the occasional movie or two being hooked up to the big screen, so hdmi output would be nice but not necessarily needed. Price point I would like to keep it around 500 but max would be 700. I'm located in the states, would prefer to stick w/ windows since thats what I know, plus I think mac is out of my pricepoint. Thanks